Simplify the following expression: $y = \dfrac{21k^3 + 21k^2}{12k^3}$ You can assume $k \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $21k^3 + 21k^2 = (3\cdot7 \cdot k \cdot k \cdot k) + (3\cdot7 \cdot k \cdot k)$ The denominator can be factored: $12k^3 = (2\cdot2\cdot3 \cdot k \cdot k \cdot k)$ The greatest common factor of all the terms is $3k^2$ Factoring out $3k^2$ gives us: $y = \dfrac{(3k^2)(7k + 7)}{(3k^2)(4k)}$ Dividing both the numerator and denominator by $3k^2$ gives: $y = \dfrac{7k + 7}{4k}$